Short Integer Research Articles

Assessing the feasibility of quantum learning algorithms for noisy linear problems

Quantum algorithms for solving noisy linear problems are reexamined, under the same assumptions taken from the existing literature. The findings of this work include on the one hand extended applicability of the quantum Fourier transform to the ring learning with errors problem which has been left open by Grilo et al., who first devised a polynomial-time quantum algorithm for solving noisy linear problems with quantum samples. On the other hand, this paper also shows there exist efficient classical algorithms for short integer solution and size-reduced learning with errors problems if the quantum samples used by the previous studies are given.

Lattice-based strong designated verifier signature with non-delegatability

Strong designated verifier signature (SDVS) is a special type of digital signatures which provides authentication of a message without providing non-repudiation property. More specifically, SDVS can enable that it is impossible for any entity, other than the designated verifier, to recognize the validity of a given signature. Although there have been several proposals of lattice-based SDVS schemes since the first non-quantum resistant scheme proposed by Jakobsson et al. at EUROCRYPT 1996, all the existing lattice-based ones cannot achieve a security notion called non-delegatablity (ND), which was an essential property introduced by Lipmaa et al. at ICALP 2005 when considering an SDVS in scenarios where the responsibility of the signer is important and the signing rights cannot be delegated to another entity. Therefore, in this work, we provide the first lattice-based SDVS scheme that offers non-delegatablity (i.e., neither the signer nor the designated verifier can delegate the signing rights to other entities without the revealment of their corresponding private keys), and thus, resolve a prominent open problem posed by previous works. Moreover, we achieve this non-trivial feat in a relatively simple manner. Starting with Lyubashevsky’s lattice signatures without trapdoors at EUROCRYPT 2012 - which is arguably the first practical alternative method in general lattices for designing digital signatures not adopting the “hash-and-sign” methodology, we introduce simple-but-insightful tweaks allowing to upgrade it directly into an SDVS with non-delegatablity. The scheme satisfies the strong security requirements of Lipmaa et al.’s model and is proven secure in the random oracle model under the short integer solution (SIS) and the learning with errors (LWE) assumptions.

Towards tightly secure short linearly homomorphic signatures

In ASIACRYPT 2016, Boyen and Li proposed an almost tightly secure short signature scheme based on pseudorandom function and the hardness assumption of short integer solution (SIS), and left it as an open problem to make it homomorphic. In this paper, we solve this problem with the same assumptions.

Lattice-Based Post-Quantum Public Key Encryption Scheme Using ElGamal’s Principles

Modern technologies like quantum and cloud computing have reshaped computing, offering immense power and scalability. While beneficial, they also challenge the security of traditional cryptographic systems. Quantum computing threatens RSA and ECC with algorithms like Shor’s algorithm, which can accelerate computations exponentially. This risks exposing these systems to attacks, necessitating quantum-resistant cryptography. Cloud computing poses data security concerns, requiring robust cryptographic mechanisms and access controls. Lattice-based cryptography, leveraging problems like the Short Integer Solution (SIS), emerges as a solution. This paper presents a novel quantum-resistant public key encryption scheme based on ElGamal and SIS, ensuring security against quantum and classical threats in modern cryptographic environments.

Identity-based chameleon hash from lattices

Identity-based chameleon hash (IBCH) is a cryptographic primitive with nice properties. IBCH equips each user with a trapdoor and the hash values can be publicly evaluated w.r.t. the identity of any user. On the one hand, it is hard to find collisions for the hash values without the user’s trapdoor. On the other hand, with the help of the user’s trapdoor, finding collisions becomes easy. An important application of IBCH is to upgrade an identity-based signature (IBS) scheme to an on-line/off-line identity-based signature (OO-IBS) scheme. OO-IBS is a useful tool to provide authenticity in lightweight smart devices, since it only involves light on-line computations and does not need key certificate. Up to now, there are many IBCH constructions from traditional number-theoretic assumptions like RSA, CDH, etc. However, none of the existing IBCH schemes achieve the post-quantum security in the standard model. In this paper, we propose a new IBCH scheme from lattices. The security of our IBCH is reduced to a well-accepted lattice-based assumption – the Short Integer Solution (SIS) assumption in the standard model. Our work provides the first post-quantum solution to IBCH in the standard model.

Module lattice based post quantum secure blockchain empowered vehicle to vehicle communication in the internet of vehicles

The importance of vehicle-to-vehicle (V2V) communication is increasing due to high rate of accidents and advancements in information exchange system. The V2V communication facilitates vehicles to exchange real-time informations about their surrounding, such as nearby vehicle, pedestrian, and road hazard. These type of informations are very helpful to detect potential collision, warn driver of imminent danger, and take advanced measure to avoid accident. Both security and privacy of user participating in the vehicular networking system depends upon reliable data transmission system. The suggested approaches must have minimal processing complexity and be unaffected by latency problems due to the scalability of V2V connection. This paper contains module lattice based quantum safe blockchain empowered authentication framework for autonomous vehicle communication system. This framework uses blockchain that is always contains multiple nodes, then we need an aggregation technique to provide authenticity to the system. The proposed framework provides authenticity to the system based on two assumptions, (1) Module Learning With Error and (2) Module Short Integer Solution. The proposed framework is quantum safe, provides high latency and throughput.

A new lattice-based password authenticated key exchange scheme with anonymity and reusable key.

In this article, we propose a novel bilateral generalization inhomogenous short integer solution (BiGISIS)-based password-authenticated key exchange (PAKE) scheme for post-quantum era security. The hardness assumption of the constructed PAKE is based on newly proposed hard lattice problem, BiGISIS. The main aim of this article is to provide a solution for the post-quantum secure PAKE scheme, which is one of the open problems in the literature. The proposed PAKE is the first BiGISIS-based PAKE that satisfies anonymity and reusable key features. The bilateral-pasteurization (BiP) approach is used to obtain the reusable key, and anonymity is achieved thanks to the additional identity components and hash functions. The reusable key structure reduces the time in the key generation, and anonymity prevents illegal user login attempts. The security analysis is done by following the real-or-random (RoR) model assumptions. As a result of security examinations, perfect forward secrecy (PFS) and integrity are satisfied, and the resistance against eavesdropping, manipulation-based attack (MBA), hash function simulation, impersonation, signal leakage attack (SLA), man-in-the-middle (MitM), known-key security (KKS), and offline password dictionary attack (PDA) is captured. According to the comparison analysis, the proposed PAKE is the first SLA-resistant lattice-based PAKE with reusable key and anonymity properties.

A module lattice based construction of post quantum secure blockchain architecture

AbstractThe Fiat–Shamir with Aborts paradigm of Lyubashevsky introduced efficient lattice based signatures. A lattice‐based signature is used to design post quantum secure blockchain architecture. But, a blockchain is always consisting of multiple nodes, and then we need an efficient aggregate signature to verify nodes in one‐step. We have designed a blockchain using module lattices. Blockchain security relies upon two assumptions, (1) module learning with errors and (2) module short integer solution. The proposed design ensures security against quantum attacks. The design is simulated in ns‐3 to capture latency and throughput, respectively.

Lattice-Based Group Signature with Message Recovery for Federal Learning

Federal learning and privacy protection are inseparable. The participants in federated learning need to be the targets of privacy protection. On the other hand, federated learning can also be used as a tool for privacy attacks. Group signature is regarded as an effective tool for preserving user privacy. Additionally, message recovery is a useful cryptographic primitive that ensures message recovery during the verification phase. In federated learning, message recovery can reduce the transmission of parameters and help protect parameter privacy. In this paper, we propose a lattice-based group signature with message recovery (GS-MR). We then prove that the GS-MR scheme has full anonymity and traceability under the random oracle model, and we reduce anonymity and traceability to the hardness assumptions of ring learning with errors (RLWE) and ring short integer solution (RSIS), respectively. Furthermore, we conduct some experiments to evaluate the sizes of key and signature, and make a performance comparison between three lattice-based group signature schemes and the GS-MR scheme. The results show that the message–signature size of GS-MR is reduced by an average of 39.17% for less than 2000 members.

Post‐quantum identity‐based authenticated multiple key agreement protocol

AbstractAuthenticated multiple key agreement (AMKA) protocols provide participants with multiple session keys after one round of authentication. Many schemes use Diffie–Hellman or authenticated key agreement schemes that rely on hard integer factorizations that are vulnerable to quantum algorithms. Lattice cryptography provides quantum resistance to authenticated key agreement protocols, but the certificate always incurs excessive public key infrastructure management overhead. Thus, a lightweight lattice‐based secure system is needed that removes this overhead. To answer this need, we provide a two‐party lattice‐ and identity‐based AMKA scheme based on bilateral short integer or computational bilateral inhomogeneous small integer solutions, and we provide a security proof based on the random oracle model. Compared with existing AMKA protocols, our new protocol has higher efficiency and stronger security.

A Verifiable Multi-Secret Sharing Scheme Based on Short Integer Solution

A Verifiable Multi-Secret Sharing Scheme Based on Short Integer Solution

Identity-Based Proxy Signature with Message Recovery over NTRU Lattice

Proxy signature is one of the important primitives of public-key cryptography and plays an essential role in delivering security services in modern communications. However, existing post quantum proxy signature schemes with larger signature sizes might not be fully practical for some resource-constrained devices (e.g., Internet of Things devices). A signature scheme with message recovery has the characteristic that part or all of the message is embedded in the signature, which can reduce the size of the signature. In this paper, we present a new identity-based proxy signature scheme over an NTRU lattice with message recovery (IB-PSSMR), which is more efficient than the other existing identity-based proxy signature schemes in terms of the size of the signature and the cost of energy. We prove that our scheme is secure under a Short Integer Solution (SIS) assumption that is as hard as approximating several worst-case lattice problems in the random oracle model. We also discussed some application scenarios of IB-PSSMR in blockchain and Internet of Things (IOT). This paper provides a new idea for the design of lattice signature schemes in low resource constrained environments.

A fully dynamic forward-secure group signature from lattice

A forward-secure group signature (FSGS) ensures the unforgeability of signatures in the past time period despite signing secret key is leaked in the current time period. As we know, traditional FSGS schemes are mostly relying on number-theoretic assumptions unable to resist quantum attacks. Therefore, we present an efficient lattice-based fully dynamic (i.e. users can flexibly join or quit the group) forward-secure group signature (DFSGS) by combining an improved version of FSGS scheme proposed by Ling. Based on an efficient zero-knowledge argument, we construct argument of knowledge of the committed value and the plaintext that help with privacy protection. Our DFSGS scheme is proved to be anonymous and forward-secure traceable relying on short integer solution and learning with errors assumptions in random oracle model. Moreover, the lengths of group public key and signature of our DFSGS scheme have been improved, and the length of user secret key has no connection with the quantity of group members.

A novel identity-based multi-signature scheme over NTRU lattices

Multi-signature is an important technology to compress multiple signatures on the common message into a compact one, thereby reducing the consumption of storage space and transmission bandwidth. Such a cryptographic primitive is widely used in financial applications such as blockchain which requires multiple keys to authorize a transaction. With the advent of quantum computers, traditional multi-signature schemes may no longer be secure as their underlying security assumptions (e.g. RSA or discrete logarithm problems) may not hold anymore. In this paper, we propose a novel identity-based multi-signature (IBMS) scheme over NTRU lattices, which is secure against the attacks of quantum computers. To the best of our knowledge, it is the first lattice-based IBMS scheme. We show that our scheme is provably secure in the random oracle model based on the ring version of the short integer solution assumption (Ring-SIS). Compared with the closely related works in the literature, our scheme enables the signer to select its system identity (such as email address, physical IP address, and etc.) as the public key, which effectively alleviates the certificate management problem in the PKI setting, and takes the advantage of discrete Gaussian distribution instead of uniform distribution to generate secret signing keys and multi-signatures. Besides, our scheme does not require all the system users to setup a trusted common string, which further simplifies the deployment of our scheme in practice.

A novel communication‐aware adaptive key management approach for ensuring security in IoT networks

AbstractInternet of Things (IoT) encompasses heterogeneous communication devices and wireless technologies to provide ubiquitous access using end‐user devices. It operates on a common website for connecting versatile devices with seamless communication, data access and sharing. Communication through wireless medium requires enormous security features to protect both public and private data across different interconnected resources. Therefore, in this article, a communication‐aware adaptive key management (CAKM) is proposed to ensure two levels of security in IoT communication. The two‐levels of security include both device and message that is facilitated using certificate authority and key management. By exploiting the benefits of hyper elliptic curve cryptography (HECC), the communication‐aware adaptive key management ensures message authentication for the device requests. Initially, the device requests are classified on the basis of its service time and correlated to the time‐to‐live period of the certificate. The proposed method attains low computational time 10.9%, 30.2%, and 54.3%, high security level 10.9%, 30.2%, and 54.3%, high successful message rate 10.9%, 30.2%, and 54.3% and low key agreement time 10.9%, 30.2%, and 54.3% when compared to the three existing methods, such as bilateral generalization inhomogeneous short integer solution (Bi‐GISIS)‐based key management in IoT security (Bi‐GISIS‐IoT), hyper elliptic curve based public key cryptosystem in IoT security (HCCPK‐IoT) and enhanced symmetric key‐based authentication in IoT security (ESKA‐IoT). Finally, the proposed method provides an efficient security with low computational time.

A forward-secure and efficient authentication protocol through lattice-based group signature in VANETs scenarios

Message authentication has been a research hotspot in current vehicular ad hoc networks (VANETs). Many researchers adopt group signatures based on number-theoretic assumptions to authenticate the vehicular users’ identities. Nevertheless, the classical group signature is vulnerable to quantum computing attacks and without considering the negative consequences of secret key disclosure. In this paper, to address these problems, we propose a novel group signature protocol for authentication in VANETs, which is based on lattice cryptography to achieve quantum-resistance and Bonsai-tree signature architecture to achieve forward security. Our scheme is proven secure in terms of traceability, anonymity, and forward-security under the Short Integer Solution (SIS) and Learning With Errors (LWE) hardness. Through comprehensive performance evaluation, we demonstrate that the storage overhead of our scheme is relatively diminutive and the computation cost of the sign and verify algorithms are efficient and practical compared with other existing schemes.

Revocable identity-based fully homomorphic signature scheme with signing key exposure resistance

Fully homomorphic signature schemes in identity-based settings can provide authenticity, homomorphism, and non-repudiation as do traditional digital signatures, while simplifying the public key infrastructure (PKI) requirements, in which each user in the system can use his or her identity as a public key. As identity-based systems (IBS) have a natural link between unique identity information and the user, allowing user revocation is usually more difficult in IBS than in PKI settings. Although several revocable identity-based fully homomorphic signature (RIBFHS) schemes have been proposed, these schemes are vulnerable to signing key exposure. With this study, we are the first to consider a realistic threat signing key exposure in RIBFHS systems. In addition, we introduce a new security definition of RIBFHS with signing key exposure resistance. Then, we employ Agrawal’s left–right lattices and delegation technology in fixed dimensions to construct a new RIBFHS scheme over the lattice with regularly broadcasted update keys, which not only resists signing key exposure, but also meets scalability and context hiding properties. Finally, we prove that our construction is existentially unforgeable against chosen message attacks under the standard short integer solution (SIS) assumption in the random oracle model.

Aggregable Confidential Transactions for Efficient Quantum-Safe Cryptocurrencies

Confidential Transactions (CT) hide coin amounts even from verifiers without the help of trusted third parties. Aggregable CTs are a scalable category of CTs with “spent coin record trimming”. For example, if Alice sends coins to Bob, who had sent similar coins to Charles, the aggregated transaction shows only that Alice sent coins to Charles by deleting Bob’s coin records. Since the number of spent coin records grows linearly with the number of transactions, faster than the number of accounts, cash systems based on aggregable CTs are highly scalable. However, existing quantum-safe aggregable CT protocols have large unspent coin records, and existing efficient aggregable CTs are vulnerable to quantum attacks. We introduce two aggregable CT protocols, based on new efficient homomorphic zero-knowledge proofs, from either the plain or Module Short Integer Solution (SIS and MSIS) problems, both believed to be secure against quantum adversaries. We further implement the MSIS-based aggregable CT protocol as a C library. Our experiments on 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> transactions show that aggregation reduces the cash system’s size by 40%–54% when the output/input rate is in the range 1/1–2/1. For example, a cash system of 1.73 GB can be reduced to 0.98 GB when the output/input rate is 1.5, which has been the historical real-world average rate.

Policy-Based Group Signature Scheme from Lattice

Although the existing group signature schemes from lattice have been optimized for efficiency, the signing abilities of each member in the group are relatively single. It may not be suitable for complex applications. Inspired by the pioneering work of Bellare and Fuchsbauer, we present a primitive called policy-based group signature. In policy-based group signatures, group members can on behalf of the group to sign documents that meet their own policies, and the generated signatures will not leak the identity and policies of the signer. Moreover, the group administrator is allowed to reveal the identity of signer when a controversy occurs. Through the analysis of application scenarios, we concluded that the policy-based group signature needs to meet two essential security properties: simulatability and traceability. And we construct a scheme of policy-based group signature from lattice through techniques such as commitment, zero-knowledge proof, rejection sampling. The security of our scheme is proved to be reduced to the module short integer solution (MSIS) and module learning with errors (MLWE) hard assumptions. Furthermore, we make a performance comparison between our scheme and three lattice-based group signature schemes. The result shows that our scheme has more advantages in storage overhead and the sizes of key and signature are decreased roughly by 83.13%, 46.01%, respectively, compared with other schemes.

Approximating Closest Vector Problem in ℓ∞-Norm Revisited

Abstract The security of most lattice-based cryptography schemes are based on two computational hard problems which are the short integer solution (SIS) and learning with errors (LWE) problems. The computational complexity of SIS and LWE problems are related to approximating shortest vector problem and bounded distance decoding (BDD) problem. Approximating BDD is a special case of approximating closest vector problem (CVP). In this paper, we revisit the study for approximating CVP. We give a proof that approximating the CVP over $\ell _\infty $-norm (CVP$_\infty $) within any constant factor is NP-hard. The result is obtained by the gap-preserving reduction from Min Total Label Cover problem in $\ell _1$-norm to to CVP$_\infty $. This proof is simpler than known proofs [ 10].